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Theorem dfiun2g 4091
 Description: Alternate definition of indexed union when is a set. Definition 15(a) of [Suppes] p. 44. (Contributed by NM, 23-Mar-2006.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
dfiun2g
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem dfiun2g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfra1 2724 . . . . . 6
2 rsp 2734 . . . . . . . 8
3 clel3g 3041 . . . . . . . 8
42, 3syl6 31 . . . . . . 7
54imp 419 . . . . . 6
61, 5rexbida 2689 . . . . 5
7 rexcom4 2943 . . . . 5
86, 7syl6bb 253 . . . 4
9 r19.41v 2829 . . . . . 6
109exbii 1589 . . . . 5
11 exancom 1593 . . . . 5
1210, 11bitri 241 . . . 4
138, 12syl6bb 253 . . 3
14 eliun 4065 . . 3
15 eluniab 3995 . . 3
1613, 14, 153bitr4g 280 . 2
1716eqrdv 2410 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1547   wceq 1649   wcel 1721  cab 2398  wral 2674  wrex 2675  cuni 3983  ciun 4061 This theorem is referenced by:  dfiun2  4093  dfiun3g  5089  iunexg  5954  uniqs  6931  ac6num  8323  iunopn  16934  pnrmopn  17369  cncmp  17417  ptcmplem3  18046  iunmbl  19408  voliun  19409  sigaclcuni  24462  sigaclcu2  24464  sigaclci  24476  measvunilem  24527  meascnbl  24534 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ral 2679  df-rex 2680  df-v 2926  df-uni 3984  df-iun 4063
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